44ed7/3
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Prime factorization
22 × 11
Step size
33.338¢
Octave
36\44ed7/3 (1200.17¢) (→9\11ed7/3)
Twelfth
57\44ed7/3 (1900.26¢)
Consistency limit
8
Distinct consistency limit
4
 |
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| ← 43ed7/3 | 44ed7/3 | 45ed7/3 → |
44 equal divisions of 7/3 (abbreviated 44ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 44 equal parts of about 33.3 ¢ each. Each step represents a frequency ratio of (7/3)1/44, or the 44th root of 7/3.
Intervals
| Steps | Cents | Approximate Ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 33.338 | |
| 2 | 66.676 | 27/26, 28/27, 29/28 |
| 3 | 100.014 | 17/16, 18/17, 19/18 |
| 4 | 133.352 | 13/12, 14/13 |
| 5 | 166.69 | 11/10 |
| 6 | 200.028 | 9/8 |
| 7 | 233.366 | 8/7, 31/27 |
| 8 | 266.704 | 7/6 |
| 9 | 300.042 | 19/16, 31/26 |
| 10 | 333.38 | 17/14, 23/19, 29/24 |
| 11 | 366.718 | 21/17, 26/21 |
| 12 | 400.056 | 24/19, 29/23 |
| 13 | 433.394 | 9/7 |
| 14 | 466.732 | 17/13, 21/16 |
| 15 | 500.07 | 4/3 |
| 16 | 533.408 | 15/11, 19/14 |
| 17 | 566.746 | 18/13 |
| 18 | 600.084 | 17/12, 24/17 |
| 19 | 633.422 | 13/9, 23/16 |
| 20 | 666.76 | 22/15, 28/19 |
| 21 | 700.097 | 3/2 |
| 22 | 733.435 | 26/17, 29/19 |
| 23 | 766.773 | 14/9 |
| 24 | 800.111 | 19/12, 27/17 |
| 25 | 833.449 | 21/13 |
| 26 | 866.787 | 28/17 |
| 27 | 900.125 | 27/16 |
| 28 | 933.463 | 12/7 |
| 29 | 966.801 | 7/4 |
| 30 | 1000.139 | 16/9 |
| 31 | 1033.477 | 20/11, 29/16 |
| 32 | 1066.815 | 13/7, 24/13 |
| 33 | 1100.153 | 17/9 |
| 34 | 1133.491 | 27/14 |
| 35 | 1166.829 | |
| 36 | 1200.167 | 2/1 |
| 37 | 1233.505 | |
| 38 | 1266.843 | 27/13, 29/14 |
| 39 | 1300.181 | 17/8 |
| 40 | 1333.519 | 13/6, 28/13 |
| 41 | 1366.857 | 11/5 |
| 42 | 1400.195 | 9/4 |
| 43 | 1433.533 | 16/7 |
| 44 | 1466.871 | 7/3 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.2 | -1.7 | +0.3 | +14.1 | -1.5 | -1.7 | +0.5 | -3.4 | +14.2 | +15.9 | -1.4 |
| Relative (%) | +0.5 | -5.1 | +1.0 | +42.2 | -4.6 | -5.1 | +1.5 | -10.1 | +42.7 | +47.8 | -4.1 | |
| Steps (reduced) |
36 (36) |
57 (13) |
72 (28) |
84 (40) |
93 (5) |
101 (13) |
108 (20) |
114 (26) |
120 (32) |
125 (37) |
129 (41) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -6.6 | -1.5 | +12.4 | +0.7 | -4.3 | -3.2 | +3.2 | +14.4 | -3.4 | +16.1 | +5.8 |
| Relative (%) | -19.7 | -4.6 | +37.2 | +2.0 | -12.8 | -9.6 | +9.6 | +43.2 | -10.1 | +48.3 | +17.4 | |
| Steps (reduced) |
133 (1) |
137 (5) |
141 (9) |
144 (12) |
147 (15) |
150 (18) |
153 (21) |
156 (24) |
158 (26) |
161 (29) |
163 (31) | |